The structure of the s -degrees contained within a single e -degree

Annals of Pure and Applied Logic 160 (1):13-21 (2009)
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Abstract

For any enumeration degree let be the set of s-degrees contained in . We answer an open question of Watson by showing that if is a nontrivial -enumeration degree, then has no least element. We also show that every countable partial order embeds into . Finally, we construct -sets A and B such that B≤eA but for every X≡eB, XsA

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Citations of this work

Bounded enumeration reducibility and its degree structure.Daniele Marsibilio & Andrea Sorbi - 2012 - Archive for Mathematical Logic 51 (1-2):163-186.

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References found in this work

Jumps of quasi-minimal enumeration degrees.Kevin McEvoy - 1985 - Journal of Symbolic Logic 50 (3):839-848.
Then-rea enumeration degrees are dense.Alistair H. Lachlan & Richard A. Shore - 1992 - Archive for Mathematical Logic 31 (4):277-285.
Strong Enumeration Reducibilities.Roland Sh Omanadze & Andrea Sorbi - 2006 - Archive for Mathematical Logic 45 (7):869-912.
Enumeration Reducibility Using Bounded Information: Counting Minimal Covers.S. Barry Cooper - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (6):537-560.

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